Advanced Audio Properties:
Use one track for streaming and the other for recording. Assign things accordingly.
Settings -> Output:
Select one track to stream and a different one to record, according to your assignments above.
If you're using the Simple settings, then the stream is locked to Track 1, but the recording still has options.
You can even record multiple tracks if you want, and keep things even more separate. Then you can mix them later and not live.
